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作者机构:Columbia Univ Dept Ind Engn & Operat Res IEOR New York NY 10027 USA
出 版 物:《SIAM JOURNAL ON FINANCIAL MATHEMATICS》 (SIAM金融数学杂志)
年 卷 期:2015年第6卷第1期
页 面:467-486页
核心收录:
学科分类:1202[管理学-工商管理] 07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金:NSF [DMS-1016571] DOE [DE-FG02-08ER25856] ONR [N000140310514] Directorate For Engineering Div Of Civil, Mechanical, & Manufact Inn Funding Source: National Science Foundation
主 题:large scale portfolio optimization coherent risk measures first-order algorithms
摘 要:We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value-at-risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs;hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient;it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.